Question: A certain company's main source of income is selling socks. The company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by: $P(x)=-3(x-5)^2+12$ What is the maximum profit that the company can earn?
Solution: The company's profit is modeled by a quadratic function, whose graph is a parabola. The maximum profit is reached at the vertex. So in order to find the maximum profit, we need to find the vertex's $y$ -coordinate. The function $P(x)$ is given in vertex form. The vertex of $-3(x-{5})^2{+12}$ is at $({5},{12})$. In conclusion, the maximum profit is $12$ million dollars.